INTERNATIONAL JOURNAL OF GEOLOGY Issue 3, Volume 4, 2010 Numerical Convection of Viscoelastic Magnetic Flows Past a Backward Facing Step Channel Cheng-Hsing Hsu, Kuang-Yung Kung, Shu-Yu Hu [email protected] magnetic visco-elastic fluid. The Maxwell model must be more Abstract—Numerical simulation presented viscoelastic magnetic than the introduction of a relaxation time, the stress tensor as flow past a backward facing step channel. The parameters of independent variables, and this model is mainly used in large Richardson Number, Reynolds Number, elastic coefficient, buoyancy magnetic visco-elastic fluid. effects and magnetic field parameters were studied. The larger The main purpose of this paper is to use numerical simulation buoyancy effect was along with a larger Richardson Number. Transient coexistence of multiple second recirculation zone appear in to explore the magnetic field fixed at the high Richardson downstream. The four symmetry vortexes appeared on the upper and Number of cases. The second model visco-elastic magnetic lower plate. The oscillation phenomena were similar to Karman fluid flow in the backward facing step is expected that the vortex. Under the same Richardson Number, Reynolds Number, and visco-elastic magnetic fluid in the post flow to the backward the elastic coefficient, the higher the magnetic field parameters facing step to have a better understanding of the characteristics. resulted to the shorter length of the main and second recirculation Backward step of the flow phenomenon has been valued by zone. everyone. The flow fields in supersonic flow first by Hama Keywords—Buoyancy effect, Elastic coefficient, Magnetic field experiment found that supersonic fluid flow through the parameter, Viscoelastic magnetic fluid. backward facing step after the sharp corners produced by separation. The main reason for the Reynolds Number is small, I. INTRODUCTION the separation angle from near the concave production ladder. n recent years, due to the rapid development of electronics When the Reynolds Number is large, concave angle generated Iindustry, the electronics industry output has become a staple in addition to separation, will be followed by another in the of many. Visco-elastic magnetic fluid applications in the convex corner separation near the production area. industrial areas draw much attention, such as Non-Newtonian In 1975 Honji [1] observed by the experiments re-attachment fluid transport and heat transfer phenomena. The visco-elastic length increases with time to lower growth and time is about a magnetic fluid and Newtonian fluid flow characteristics have linear relationship. Armaly et [2] were also from the great differences. Scholars had established the theory of experimental and numerical methods that, when the Reynolds magnetic fluid visco-elastic foundation and processing mode, Number is greater than 420, the order form in a relatively flat and analysed the visco-elastic magnetic fluid and The area above the board has time back production. When the Newtonian fluid. The electromagnetic interference affected the Reynolds Number increased to 980, the lower plate near the working environment and quality of the products. downstream of the primary recirculation zone will also produce After the flow field of the study to the backward facing step another. The numerical results are compared with the on the Newtonian fluid, over the years has been taken seriously. experimental data; the Reynolds Number less than four Because the flow field includes the phenomenon of flow hundreds, both errors is really small. But more than this range, separation and reattachment, the flow characteristics can be three-dimensional effect by enhancing the flow field, resulting demonstrated very clearly low, and furthermore because of its in two-dimensional numerical simulation lead to considerable simple geometry and easy analysis. However, in engineering error. applications, such as positive and negative electrode membrane Durst and Pereia [3] After using the TEACH code on the fuel cell reaction between hydrogen and oxygen can also be backward facing step to do transient flow analysis, when the used to step upon the downstream vortex flow field to promote Reynolds Number equal to ten, divided off from the concave the hydrogen produced by reaction to an adequate response, and angle to start production, increase over time along the vertical then to a higher efficiency of chemical reactions purpose. ladder climbing rose. In the Reynolds Number is equal to 368, Integral equation was using the second order model and the and then the concave corner and convex corner vortex near the Maxwell model. Second mode in which all the higher order emergence of an independent, gradually increasing over time nonlinear terms to the stress tensor, that its behalf into the merge. And there have been times back on the flat area, but momentum equation. Such models are mainly used in small stable before has disappeared. There are a number of other studies, such as Sparrow and Chuck [4] through personal computers, calculation of steady forced convection flow, analysis of step height and Reynolds 64 INTERNATIONAL JOURNAL OF GEOLOGY Issue 3, Volume 4, 2010 Number on the reattachment length and the impact and return to contact length will be reduced. Abu-Milaweh [13], and others the region of thermal convection effect. Chein [5] using stream use the Doppler and cold wire anemometer to do the vertical function and vorticity equations for computing functions, with ladder of the disorder after the measurement of mixed the continuous relaxation, the first order explicit upwind finite convection experiment, found a small free stream will result in difference method and the circulation flow theory for transient turbulence intensity decreases, while the convective line analysis. position, cross-section rate and temperature difference. The John and Leone [6] to finite element analysis of the backward longer contact length with the lower heating plate, the heat facing step in steady mixed convection flow. In the ladder above transfer rate decreases. the heating plate and found that the Richardson Number of The mutant form of the researchers in terms of elastic fluids, logical investigation is equal to 9 or 16, the Reynolds Number is is a major problem, especially in corners of the deal more equal to 800, Prandtl Number is equal to 1, the ladder, there are complex than the Newtonian fluid, it is often the determining three vortex downstream plate, heating two vortex appeared on factor in numerical convergence. In addition there are board, paper, and to explore the effects of different export visco-elastic fluid heat transfer characteristics, the literature not length. Lin and Armaly [7] The TEACH code analysis of the many. Only early Vest and Arpaci [14] Herbert [15] and vertical pipe after the backward facing step steady mixed mathematical analysis of the way of a visco-elastic fluid heated convection. Found that increased buoyancy will shorten the in the flat state of stability. Hsu and Chieng [16], Chen and Teng length of re-engagement, increase in the ladder flat concave [17] while the second model of a visco-elastic fluid in a corner recirculation zone times the range. When the buoyancy continuous moving plate and a wedge on the flow of heat generated by increased starved flow, then the vertical ladder transfer analysis. Hsu and Chou [18] The visco-elastic fluid access point is located, their locations back to the highest point flow in the backward facing step phenomena, compare different of heat transfer area in contact point further downstream. The Reynolds Number and elasticity of the flow field development size and Nusselt Number of local enhanced with the buoyancy under the circumstances. Hsu et [19] also discussed the of the gain in great, although the backward facing step with the visco-elastic fluid in different Richardson Number, Reynolds analysis of flow field is highly valued, but most of Newtonian Number and elastic modulus of the backward facing step field. fluid as the main target. In Richardson Number is defined as the buoyancy effect. When For visco-elastic fluid flow field after the backward facing Richardson Number increases, the primary recirculation zone step is rarely discussed phenomenon. Only Kawabata et [8] The will increase, while the increase elasticity to reduce the scope. Maxwell model of steady-state flow phenomena found in the Thermal boundary layer flow field increases with time, same Reynolds Number, visco-elastic fluid in the lower speed gradually from the lower plate to the thickening of the internal step slower than the Newtonian fluid. In recent years, the flow field. When Richardson Number is equal to 1, elastic backward facing step after the special study areas Chan et [9] coefficient is equal to 0.001, and the Reynolds number of 50 and used the Improved Stochastic Separated Flow (ISSF) numerical 75, the reattachment length of its overshoot phenomenon. This simulation of gas - particle flow in the latter case the flow to the is no place Newtonian fluid flow characteristics. So, the backward facing step. Found its way analysis of anisotropic Richardson Number of 1, elastic coefficient of 0.001, and the particle flow disorder has a good effect. Piccolo et [10] used the Reynolds Number 75, have a steady second recirculation zone numerical simulation analysis of the primary recirculation zone exists. to the backward facing step and external fluid exchange Hsu and Kung [20] while further are adding the change of between the disturbed stream function, the paper can be found flow angle of the visco-elastic fluid on the backward facing step to the convective flow downstream due to the interaction of after the impact of transient mixed convection. Found that the disturbance associated with discontinuous shear surface caused reattachment length increases gradually as the angle increased by the periodic large-scale vortex in the backward facing step, to the maximum value and then decrease as the angle increases, the primary recirculation zone showed the coexistence of the maximum angle in the flow channel 150 or 180 degrees.